Twin-star models are squeezed
Only an extremely small part of the model's parameter space remains compatible with a twin-star scenario under the low-density ChEFT constraint, a theory-based input, and generic astrophysical data. The analysis is framed as a compatibility test against those inputs.
To make that comparison, the analysis compares three different distributions and introduces a hybrid branch. It uses TOV equations, which reconstruct radial profiles from the inferred relation between pressure and energy density, to calculate the model stars.
The radii stay close
For generic 1.4-solar-mass and 2.1-solar-mass neutron-star models, the median radii are nearly equal, at about 12 kilometres. The two cases therefore share almost the same central size estimate in the analysis.
The uncertainty around that result remains meaningful. A 95% credible radius band spans approximately 11 to 13 kilometres. The reported answer is therefore a range around the model's central radius, not a single fixed size.
The two results describe different parts of the model: the radius band summarizes star size, while the extremely small region describes how much parameter freedom remains for the twin-star scenario.
The branch test leans one way
The branch comparison is cautious in its wording. The conclusion gives a Bayes factor, a measure used to compare competing model scenarios, of 11.8 and calls the evidence against multiple disconnected branches only strong. The reported comparison leans against multiple branches without presenting that finding as a definitive exclusion.
The analysis also includes PSR J1731-347 as an observational constraint. Adding it does not change the 68% credible interval reported by the analysis. In other words, that additional input leaves the stated interval unchanged in the comparison.
Mass information changes the ceiling
Mass data affect the model's ceiling more than its size estimate. Adding the mass constraint is interpreted as substantially increasing the estimated maximum neutron-star mass while having little effect on the radius. The conclusion is therefore asymmetric: the top mass estimate moves much more than the modeled radius.
Separately, the NICER-reported radius for PSR J0437-4715 shifted to about 11.4 kilometres, with about 10% uncertainty. That value lies within the broader 11-to-13-kilometre credible band reported for the modeled radius. The two results are not the same kind of statement: one is a radius reported for a named pulsar, while the other is a model interval.
A shallow feature in the model
The analysis also finds a shallow maximum in squared sound speed, the model quantity used to track how pressure responds as density rises. Its reported central value is 0.78. Because this is a posterior result, it belongs to the model's inferred picture of dense matter rather than serving as a direct measurement.
The authors' interpretation remains restrained. They say a twin-star scenario would become even more unlikely if a more massive neutron star were observed, while the present analysis already leaves very little room for it. The result is thus a tight model constraint on twin-star possibilities, not a claim that the astrophysical question has been settled.
Paper data and sources
Original title: Size and Distance Scales in the Nucleon and in Dense Baryonic Matter
Authors: Wolfram Weise
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text